If you make a box and then grab the four corners, you can then rotate those and make twisted box. Okay, fine. However, if I try to make an insert on either the top or bottom surface of the twist it isn't working.

I'm betting it has something to do with the fact that the cube has a history state once immediately created,
but when you alter the cube, it becomes a joined/multi-surface object and does not have the ability to alter its sub-surfaces by moving any points. In fact, the points shouldn't move if adjoined by multiple joined surfaces.

You could use the Twist command, but that would make a smoothly transitioning twist. If it's a simple structure you might have to resort to using a lot of construction guides.

What would work here would be some kind of "cage" manipulation, not available yet.

Further experimentation shows that you are only able to edit structures, namely cubes, based on planes where there are no trim curves present.
The surfaces in the structure can only be four-point planes. You can Extrude a Plane, by the way, (not a trimmed plane) and manipulate its points as well.

Once you add any other complex surfaces like Fillets, then you now have compound and trimmed surfaces joined together and that cannot be simply manipulated by moving corner points.

Hi plish, try doing the Inset on the plain box first, and then use the Transform > Twist on that.

It looks like Inset is having some problem with generating offsets on the twisted side walls, so do the twisting last instead of doing it first.

It doesn't really take too much for Inset to get confused, it uses a combination of several offset operations within it, and that is not a very strong area of the geometry library that MoI uses currently. The people who develop the library have said that they have been working on an update to solid offsetting for a while now but it's still in progress.

Hi plish, also it looks like another way you can do it with your previous "twist first" method is to delete the top and bottom faces after you've done the twist and then select the now open-ended twisted box and use Construct > Planar to close off the ends with brand new planar end caps.

Probably after that the Inset will work - basically what happens is that after you do a control point manipulation on an object all surfaces that make up the object are converted from any "analytic" surfaces (specialized surface classes for specific shapes like spheres, cylinders, and planes), and instead become just a generic NURBS surface. But some processes like offsets work better when they can use analytic surfaces when possible. Deleting and putting new end caps on will make the ends to be analytic planes and that will help, and also saving the file and reloading it will cause them to become analytic surfaces as well.

I can probably fix this up so that after you do some control point manipulation any things that are planar after the point squishing can get set up with analytic surfaces again instead of those being lost as part of the control point editing process.

Michaels planar re-creation to get an "analytic" face works on a twist command twisted rectangle.
Just the last selected face direction required it. The twisty sides would do inset, as well as the bottom side.
Sometimes the inset would be "outwards," when it should have been "inwards," on the bottom side.
(Like "inside" and "outside," were backwards...?)

I've fixed this up for the next v3 beta so that after control point editing it will now automatically test for and use analytic surfaces when possible in the result, so the inset case here that failed should work in the next v3 beta without needing to do any extra steps.